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Data-Driven Tuning Parameter Selection for High-Dimensional Vector Autoregressions
No full textLasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on unknown population quantities. Furthermore, the resulting estimates and the number of variables retained in the model depend crucially on the chosen penalty level. However, there is currently no theoretically founded guidance for this choice in the context of high-dimensional time series. Instead, one resorts to selecting the penalty level in an ad hoc manner using, for example, information criteria or cross-validation. We resolve this problem by considering estimation of the perhaps most commonly employed multivariate time series model, the linear vector autoregressive (VAR) model, and propose versions of the Lasso, post-Lasso, and square-root Lasso estimators with penalization chosen in a fully data-driven way. The theoretical guarantees that we establish for the resulting estimation and prediction errors match those currently available for methods based on infeasible choices of penalization. We thus provide a first solution for choosing the penalization in high-dimensional time series models. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work
Exploring Contemporary Classification Practices:Organizing Information, Technological Change and Ideological Contestation
No full textPhase consistency test to identify type II strongly lensed gravitational-wave signals using a single event
No full textStrong-gravity precession resonances for binary systems orbiting a Schwarzschild black hole
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Retrodiction of measurement outcomes on a single quantum system revealing entanglement with its environment
No full textThe density matrix yields probabilistic information about the outcome of measurements on a quantum system, but it does not distinguish between classical randomness in the preparation of the system and entanglement with its environment. Here we show that retrodiction, employing both prior and posterior knowledge, gives rise to conditional probabilities for measurements on a single system, that can witness if it is part of a larger composite system. The degree of certainty with which one can retrodict the outcomes of multiple measurements on a system can witness both the existence and the quantitative nature of its entanglement with the environment